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Every year natural and man-made disasters cause considerable human and economic losses. It is essential to prepare for different relief operations to prevent and reduce these losses. In this paper, we propose an integrated evacuation and distribution logistic system to obtain simultaneous routing and scheduling of vehicles to evacuate people from affected areas to shelters and provide them with necessary relief commodities. We assume that shelters and vehicles have limited capacity and the demand of each affected area and distribution center could be fulfilled by more than one vehicle (split delivery). The proposed problem is formulated as a Mixed-Integer Linear Programming model with the objective of minimization of the sum of arrival times of the vehicles at affected areas, shelters, and distribution centers. We also propose a Memetic Algorithm (MA) to solve this integrated model on large-scale problems efficiently after tuning the MA parameters using the Taguchi method. The proposed model and algorithm are used to solve a case study in Tehran, the capital of Iran. The evaluation of the results shows the effectiveness of the proposed disaster relief logistic system in minimizing the total waiting time of evacuees and delivery time of supplies. The results also show that the number of relief vehicles and capacity of shelters can considerably affect the total relief time in disaster relief operations. [ABSTRACT FROM AUTHOR]